About Saudis

 
As Azimuth said, it is hard to know exactly because it is hard to find whole community of pure Afro-saudis. However, estimates are made on what the percentage of Saudis of African descends(not mixed).  CIA world fact book will tell you for instance 90% Arab, and 10% Afro-Asiatic or basically black. Is this precise? I dont' know how they got that percentage if no Saudi census so far included race as an option even!
Regarding the racial component of Saudis, you can say that most of Saudi Arabia is of homogeneous population except the Western part or the Hijaz part. What made Hijaz different is:
1- Mecca and Medina, attracting many Muslims overseas to reside there over the past 1400 years after Islam establishment.
2- Hijaz, especially Jiddah and Mecca, laid on the major trade route between Europe, Africa and Asia. Therefore, many traders of foriegn origin resided there.

Most Caucasian looking saudis are of Turkic origin or Central Asian origin. Also some can trace themselves to the Arnauts (Albanians mainly) who Mehmet Ali brought to Hijaz during his wars against the Saud family during 1850's.  Many families can be traced to their origin despite their mixture look via their last name. For instance, surnames such as Turkistani, Khojah, Tambousi, Bukhari...etc are mainly central asians originally. Daghestanis are clearly immigrants from Daghestan republic of the Russian Federation next to Chechenya. Jawis are from Jawa or Java region of Indonesia, Okashah too are Malays.  Kurdistani, Jalal aldeen, and so on are Kurds.

Finally, many Uzbek saudis existed only in the past 60 years due to immigration from the Soveit Union due to religious prosecution. They chose to reside in Hijaz for obvious reasons as the Mecca and Medina location and the previous central asian population existing there.